The following line passes through point $(5, -2)$ : $y = \dfrac{7}{6} x + b$ What is the value of the $y$ -intercept $b$ ?
Answer: Substituting $(5, -2)$ into the equation gives: $-2 = \dfrac{7}{6} \cdot 5 + b$ $-2 = \dfrac{35}{6} + b$ $b = -2 - \dfrac{35}{6}$ $b = -\dfrac{47}{6}$ Plugging in $-\dfrac{47}{6}$ for $b$, we get $y = \dfrac{7}{6} x - \dfrac{47}{6}$. ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${11}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ ${\llap{-}11}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${11}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ ${\llap{-}11}$ $(5, -2)$